Surfaces, heterogeneous, thermodynamics

Many simple systems that could be expected to form ideal Hquid mixtures are reasonably predicted by extending pure-species adsorption equiUbrium data to a multicomponent equation. The potential theory has been extended to binary mixtures of several hydrocarbons on activated carbon by assuming an ideal mixture (99) and to hydrocarbons on activated carbon and carbon molecular sieves, and to O2 and N2 on 5A and lOX zeoHtes (100). Mixture isotherms predicted by lAST agree with experimental data for methane + ethane and for ethylene + CO2 on activated carbon, and for CO + O2 and for propane + propylene on siUca gel (36). A statistical thermodynamic model has been successfully appHed to equiUbrium isotherms of several nonpolar species on 5A zeoHte, to predict multicomponent sorption equiUbria from the Henry constants for the pure components (26). A set of equations that incorporate surface heterogeneity into the lAST model provides a means for predicting multicomponent equiUbria, but the agreement is only good up to 50% surface saturation (9). 

Both extreme models of surface heterogeneity presented above can be readily used in computer simulation studies. Application of the patch wise model is amazingly simple, if one recalls that adsorption on each patch occurs independently of adsorption on any other patch and that boundary effects are neglected in this model. For simplicity let us assume here the so-called two-dimensional model of adsorption, which is based on the assumption that the adsorbed layer forms an individual thermodynamic phase, being in thermal equilibrium with the bulk uniform gas. In such a case, adsorption on a uniform surface (a single patch) can be represented as... 

In the limit of a - 0, the ideal Langmuir adsorption isotherm is obtained. See - Frumkin isotherm, and for the role of surface heterogeneity - Temkin isotherm. Refs. [i] Horanyi G (2002) Specific adsorption. State of art Present knowledge and understanding. In Bard A], Stratmann M, Gileadi M, Urbakh M (eds) Thermodynamics and electrified interfaces. Encyclopedia of electrochemistry, vol. I. Wiley-VCH Verlag, Weinheim, pp 349-382 [ii] Calvo EJ (1986) Fundamentals. The basics of electrode reactions. In Bamford CH, Compton RG (eds) Comprehensive chemical kinetics, vol. 26. Elsevier, Amsterdam, pp 1-78... 

The statistical thermodynamic treatment of the BET theory has the advantage that it provides a satisfactory basis for further refinement of the theory by, say, allowing for adsorbate-adsorbate interactions or the effects of surface heterogeneity. By making the assumptions outlined above, Steele (1974) has shown that the problems of evaluating the grand partition function for the adsorbed phase could be readily solved. In this manner, he arrived at an isotherm equation, which has the same mathematical form as Equation (4.32). The parameter C is now defined as the ratio of the molecular partition functions for molecules in the first layer and the liquid state. 

G. D. Halsey, Advances in Catalysisy 4 (1952), presents an excellent critique of the various theories of adsorption in the light of surface heterogeneity. T. L. Hill in the preceding chapter outlines the statistical mechanical and thermodynamics of the different sorption theories. 

Similar problems arise with the surface excess Gibbs energy G°, which is defined in table 1.2 in sec. 1.3. However, a number of enthalpy changes (upon adsorption, immersion, etc.) can be obtained and from them useful thermodynamic information can be deduced, see sec. 1.3. Some of these measurements contribute to the understanding of surface heterogeneity (in the energetic sense). In principle such information can also be obtained by isotherm analysis, see sec. 1.7. 

W. Rudzinski, Lee Shyi-Long, T. Panczyk, Yan Ching-Cher, A fractal approach to adsorption on heterogeneous solids surfaces. II. Thermodynamic analysis of experimental adsorption data . Journal of Physical Chemistry B, 105 10857-10866 (2001). 

The kinetics of 2D Meads phase formation are complex, because bulk diffusion of Mcgoiv, charge transfer, surface diffusion of Meads, and phase transitions within 2D Meads overlayers interfere. First order phase transitions in 2D Meads overlayers are determined by the thermodynamic stability of 2D Meads phases, kinetic parameters, and surface heterogeneities. Clear experimental evidence for higher order phase transitions in Me UPD systems does not yet exist. 

The calorimetric studies of the surface heterogeneity of oxides were initiated half a century ago, and experimental findings as well as their theoretical interpretation have been recently reviewed by Rudzinski and Everett [2]. The last two decades have brought a true Renaissance of adsorption calorimetry. A new generation of fully automatized and computerized microcalorimeters has been developed, far more accurate and easy to manipulate. This was stimulated by the still better recognized fact that calorimetric data are much more sensitive to the nature of an adsorption system than adsorption isotherm for instance. It is related to the fact that calorimetric effects are related to temperature derivatives of appropriate thermodynamic functions, and tempearture appears generally... 

This commentary on the current status of research on heats of immersion begins where our review written in 1958 concludes [6]. The classification of heats of immersion of solids into liquids as a function of precoverage is expanded to include two new types of curves. Several difficulties in heat of immersion research are discussed. Then, current applications of heats of immersion to determine the average polarity of solid surfaces, heterogeneities on solid surfaces, wetting by surfactants, hydrophilicity of solid surfaces, and thermodynamics of the specific interaction of molecules from solution onto solid surfaces are described. 

The prediction of multicomponent equilibria based on the information derived from the analysis of single component adsorption data is an important issue particularly in the domain of liquid chromatography. To solve the general adsorption isotherm, Equation (27.2), Quinones et al. [156] have proposed an extension of the Jovanovic-Freundlich isotherm for each component of the mixture as local adsorption isotherms. They tested the model with experimental data on the system 2-phenylethanol and 3-phenylpropanol mixtures adsorbed on silica. The experimental data was published elsewhere [157]. The local isotherm employed to solve Equation (27.2) includes lateral interactions, which means a step forward with respect to, that is, Langmuir equation. The results obtained account better for competitive data. One drawback of the model concerns the computational time needed to invert Equation (27.2) nevertheless the authors proposed a method to minimize it. The success of this model compared to other resides in that it takes into account the two main sources of nonideal behavior surface heterogeneity and adsorbate-adsorbate interactions. The authors pointed out that there is some degree of thermodynamic inconsistency in this and other models based on similar -assumptions. These inconsistencies could arise from the simplihcations included in their derivation and the main one is related to the monolayer capacity of each component [156]. 

T wo important conclusions of the weak fluctuation approach are that, a) the energy barriers between stable configurations are much lower than those predicted by Johnson and Dettre, and that contact angle hysteresis disappears below some threshold level of surface heterogeneity. An important consequence of the latter conclusion is that determination of the thermodynamic contact angle does not require an ideal solid surface. ... 

MSL models present the correct Henry s law limit and obey the requirement of thermodynamic consistency. This model is often used to account for the effect of the size difference in the study of multicomponent adsorption equilibria [29,30]. The MSL model can be extended to include effects such as lateral interactions in the adsorbed phase as well as surface heterogeneity [80]. 

Originally postulated as an empirical equation, the Freundlich isotherm with two constants, k and , can be derived from thermodynamic or statistical considerations with the assumptions that AHads decreases exponentially with increasing surface coverage and that this decrease is due to surface heterogeneity ... 

The influence of surface heterogeneity was analyzed by Cassie and Baxter [127] (as described in Chapter 11). Deryaguin has suggested the possibility of adoption of metastable configurations as a result of surface roughness [120]. He considered the wetting line to move in a series of thermodynamically irreversible jumps from one metastable configuration to the next. 

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